[OPE-L:866] the "transformation problem"

akliman@acl.nyit.edu (akliman@acl.nyit.edu)
Mon, 29 Jan 1996 11:45:54 -0800

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Andrew here. In ope-l 792, Duncan Foley wrote that he assumes people tend to argue the "transformation problem" issues through by assuming an economy in
long run equilibrium (presumably, this means not only a uniform profit rate
and balanced reproduction but also STATIONARY PRICES) and without technical
change, because it is the simplest case analytically.

I think not. A uniform profit rate is part of the very notion of production
prices, and so is balanced reproduction, since uniform profitability requires
supplies to equal demands. (None of this implies that market prices are
equal to production prices.) But stationary price models have been adopted
because everyone has accepted Bortkiewicz's "proof" that balanced
reproduction is impossible unless prices are stationary. This is the economic
objection to Marx's alleged "failure" to "transform input prices"--it has
nothing to do with units of measurement. Bortkiewicz understood very well
that Marx's values were in money terms, as were his production prices.

Bortkiewicz's "proof" was basically repeated by Sraffa (_Production of
Commodities ..._) in a different context. Beginning from a subsistence
economy, Sraffa shows that the exchange-values that permit reproduction
are uniquely determined; hence, prices must be stationary (actually this
insn't quite true if credit relations are allowed). But after showing
this, he immediately turns to an economy that produces a surplus, and
seems to imply that prices that permit reproduction are again uniquely

But Bortkiewicz's "proof" is false, as was proved by Kliman and McGlone,
Capital and Class 35, 1988, and again by McGlone & Kliman in an article in
_Marx and Non-Equilibrium Economics_, Freeman & Carchedi (eds.), 1996. Edward
Elgar. I mention the second one because the refutation is presented more
clearly. If we assume simple reproduction (with a surplus), uniform
profitability on capital advanced, and require that all sectors' sales
equal their purchases, this is possible without stationary prices.

And this means that Sraffa is also wrong. There is no justification for
postulating that input and output prices must be identical on the ground
that these are the prices that permit reproduction.

Bortkiewicz's problem is that he thinks the payments at the start of the
period must "buy back" the outputs at the end of the period. Despite
its impeccable underconsumptionist credentials, this is absurd. Why
can't the incomes realized by sale at the end of the period buy the
outputs? Where Sraafa goes wrong is hard to say. I suspect he simply
made a false inference in moving from one case to a more complex one.
But he may also have confused a uniform profit rate on capital advanced
with a uniform profit rate on post-production replacement costs.

I also think the stationary price postulate covers over many crucial issues,
contrary to what Duncan seems to suggest. Take a simple example: Robert
Torrens said that if a farmer lays out 100 quarters of corn and 120
quarters are produced, the profit is 20 quarters. This implies a profit
rate of 20%. But Marx objected that the value of the 100 quarters can be
greater than that of the 120 quarters. (see TSV III, pp. 77-79). If
Marx was right, i.e., if a good harvest for example leads the unit value
of corn to fall sufficiently, then the profit rate is *negative*. Its
magnitude is

---------- - 1

where V(t) and V(t+1) are the unit input and output values. If 100*V(t) >
120*V(t+1), then the profit rate is negative.

The postulate of stationary prices (or values) covers up this possibility,
and leads to the conclusion that the profit rate is determined by input/
output relations, as Torrens (and Dmitriev, Sraffa, etc.) says. And this
leads to the Okishio theorem which crucially postulates equality of
input and output prices in order to "refute" Marx's law of the falling
rate of profit.

What is at issue in the postulate of stationary prices is nothing less than
whether profitability is determined by technology and the real wage rate,
exclusively, or whether it is determined by labor-time relations.

Andrew Kliman